Math Problem Statement

dados os seguintes jogos sorteados:

Sorteio 1: 1, 3, 5, 6, 8, 10, 11, 14, 16, 18, 20, 22, 24, 25
Sorteio 2: 2, 3, 4, 5, 8, 11, 12, 14, 15, 16, 18, 21, 22, 24, 25 Sorteio 3: 1, 2, 3, 6, 7, 9, 10, 13, 14, 15, 17, 20, 22, 24, 25 Sorteio 4: 1, 3, 4, 6, 7, 10, 11, 15, 17, 18, 19, 20, 21, 22, 24 Sorteio 5: 5, 6, 7, 9, 12, 13, 15, 17, 20, 21, 22, 23, 24, 25 Sorteio 6: 1, 2, 5, 6, 8, 10, 11, 13, 15, 17, 18, 19, 20, 21, 22 Sorteio 7: 1, 2, 3, 5, 7, 8, 10, 11, 13, 16, 17, 20, 21, 22, 25 Sorteio 8: 1, 2, 6, 9, 10, 12, 13, 16, 17, 18, 19, 20, 22, 24, 25 Sorteio 9: 2, 3, 7, 9, 10, 11, 12, 15, 16, 18, 19, 20, 22, 24, 25 Sorteio 10: 1, 3, 5, 6, 8, 9, 10, 12, 13, 17, 18, 19, 21, 24, 25 Sorteio 11: 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 15, 19, 24, 25

qual das seguintes sequencias gera mais acertos por jogo em média nos sorteios descritos acima?

A - 1, 3, 4, 5, 6, 8, 10, 11, 14, 16, 18, 20, 22, 24, 25
B - 1, 3, 5, 6, 8, 9, 10, 11, 13, 17, 18, 20, 22, 24, 25
C - 1, 3, 4, 5, 6, 8, 10, 11, 13, 17, 18, 20, 22, 24, 25 D - 1, 3, 5, 6, 7, 8, 10, 11, 13, 17, 18, 20, 22, 24, 25
E - 1, 3, 5, 6, 8, 9, 10, 11, 13, 15, 17, 18, 20, 22, 25

Solution

Para determinar qual sequência gera mais acertos por jogo, precisamos comparar quantos números de cada sequência aparecem em cada sorteio. Vamos fazer isso para cada uma das opções e calcular a média de acertos por jogo.

Passo 1: Contagem dos acertos por sorteio

Para cada sequência de números (A, B, C, D, E), contaremos quantos números dessa sequência aparecem em cada sorteio.

Sequência A: 1, 3, 4, 5, 6, 8, 10, 11, 14, 16, 18, 20, 22, 24, 25

Vamos contar quantos números dessa sequência aparecem em cada sorteio:

  • Sorteio 1: 1, 3, 5, 6, 8, 10, 11, 14, 16, 18, 20, 22, 24, 25 → 14 acertos
  • Sorteio 2: 2, 3, 4, 5, 8, 11, 14, 15, 16, 18, 21, 22, 24, 25 → 8 acertos
  • Sorteio 3: 1, 2, 3, 6, 7, 9, 10, 13, 14, 15, 17, 20, 22, 24, 25 → 9 acertos
  • Sorteio 4: 1, 3, 4, 6, 7, 10, 11, 15, 17, 18, 19, 20, 21, 22, 24 → 9 acertos
  • Sorteio 5: 5, 6, 7, 9, 12, 13, 15, 17, 20, 21, 22, 23, 24, 25 → 7 acertos
  • Sorteio 6: 1, 2, 5, 6, 8, 10, 11, 13, 15, 17, 18, 19, 20, 21, 22 → 10 acertos
  • Sorteio 7: 1, 2, 3, 5, 7, 8, 10, 11, 13, 16, 17, 20, 21, 22, 25 → 10 acertos
  • Sorteio 8: 1, 2, 6, 9, 10, 12, 13, 16, 17, 18, 19, 20, 22, 24, 25 → 9 acertos
  • Sorteio 9: 2, 3, 7, 9, 10, 11, 12, 15, 16, 18, 19, 20, 22, 24, 25 → 10 acertos
  • Sorteio 10: 1, 3, 5, 6, 8, 9, 10, 12, 13, 17, 18, 19, 21, 24, 25 → 9 acertos
  • Sorteio 11: 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 15, 19, 24, 25 → 9 acertos

Média de acertos da Sequência A: 14+8+9+9+7+10+10+9+10+9+911=10511=9,55 acertos por sorteio\frac{14 + 8 + 9 + 9 + 7 + 10 + 10 + 9 + 10 + 9 + 9}{11} = \frac{105}{11} = 9,55 \text{ acertos por sorteio}

Sequência B: 1, 3, 5, 6, 8, 9, 10, 11, 13, 17, 18, 20, 22, 24, 25

  • Sorteio 1: 1, 3, 5, 6, 8, 10, 11, 14, 16, 18, 20, 22, 24, 25 → 14 acertos
  • Sorteio 2: 2, 3, 4, 5, 8, 11, 14, 15, 16, 18, 21, 22, 24, 25 → 8 acertos
  • Sorteio 3: 1, 2, 3, 6, 7, 9, 10, 13, 14, 15, 17, 20, 22, 24, 25 → 9 acertos
  • Sorteio 4: 1, 3, 4, 6, 7, 10, 11, 15, 17, 18, 19, 20, 21, 22, 24 → 9 acertos
  • Sorteio 5: 5, 6, 7, 9, 12, 13, 15, 17, 20, 21, 22, 23, 24, 25 → 7 acertos
  • Sorteio 6: 1, 2, 5, 6, 8, 10, 11, 13, 15, 17, 18, 19, 20, 21, 22 → 10 acertos
  • Sorteio 7: 1, 2, 3, 5, 7, 8, 10, 11, 13, 16, 17, 20, 21, 22, 25 → 10 acertos
  • Sorteio 8: 1, 2, 6, 9, 10, 12, 13, 16, 17, 18, 19, 20, 22, 24, 25 → 9 acertos
  • Sorteio 9: 2, 3, 7, 9, 10, 11, 12, 15, 16, 18, 19, 20, 22, 24, 25 → 10 acertos
  • Sorteio 10: 1, 3, 5, 6, 8, 9, 10, 12, 13, 17, 18, 19, 21, 24, 25 → 9 acertos
  • Sorteio 11: 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 15, 19, 24, 25 → 9 acertos

Média de acertos da Sequência B: 14+8+9+9+7+10+10+9+10+9+911=10511=9,55 acertos por sorteio\frac{14 + 8 + 9 + 9 + 7 + 10 + 10 + 9 + 10 + 9 + 9}{11} = \frac{105}{11} = 9,55 \text{ acertos por sorteio}

Sequência C: 1, 3, 4, 5, 6, 8, 10, 11, 13, 17, 18, 20, 22, 24, 25

  • Sorteio 1: 1, 3, 5, 6, 8, 10, 11, 14, 16, 18, 20, 22, 24, 25 → 14 acertos
  • Sorteio 2: 2, 3, 4, 5, 8, 11, 14, 15, 16, 18, 21, 22, 24, 25 → 8 acertos
  • Sorteio 3: 1, 2, 3, 6, 7, 9, 10, 13, 14, 15, 17, 20, 22, 24, 25 → 9 acertos
  • Sorteio 4: 1, 3, 4, 6, 7, 10, 11, 15, 17, 18, 19, 20, 21, 22, 24 → 9 acertos
  • Sorteio 5: 5, 6, 7, 9, 12, 13, 15, 17, 20, 21, 22, 23, 24, 25 → 7 acertos
  • Sorteio 6: 1, 2, 5, 6, 8, 10, 11, 13, 15, 17, 18, 19, 20, 21, 22 → 10 acertos
  • Sorteio 7: 1, 2, 3, 5, 7, 8, 10, 11, 13, 16, 17, 20, 21,

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Math Problem Analysis

Mathematical Concepts

Statistics
Averages
Set Theory

Formulas

Average formula: (sum of values) / (number of values)

Theorems

Basic principles of set intersection and counting

Suitable Grade Level

Grades 9-11

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